Transcript FEL and Accelerator Physics

Free Electron Laser
and Accelerator Physics
A.M. Kondratenko
GOO “Zaryad”, Novosibirsk
The development of coherent radiation sources on a principle of the
electron laser (FEL) is based on the accelerator technique. On the one hand
FEL stimulates development of accelerator technique, makes special
requirement to parameters of an electron bunch, and on the other hand
opens new possibilities in the high-energy physics.
The usage of FEL for obtaining of the high-energy polarized beams,
for acceleration of particles with high rate, for obtaining of high energy -
colliding beams with high luminosity are discussed here. Special instability
Coulomb interaction of particles in the beam can be used for fast coherent
electron cooling.
Overview is based on works
Yaroslav Derbenev, Anatoliy Kondratenko and Evgeny Saldin
published in 1979-1985 years.
1) Generation of Coherent Radiation by a Relativistic Electron Beam in an Undulator.
Dokl.Akad.Nauk. SSSR v.249 p 843(1979); Part. Accel. v.10, p.207 (1980);
Zhurnal Tech. Fiz. v.51 p. 1633 (1981).
2) On the Linear Theory of Free Electron Lasers with Fabry-Perot Cavities.
Zhurnal Tech. Fiz. v.52 p. 309 (1982).
3) Polarization of the electron beam in a storage ring by circularly -polarized
electromagnetic wave. Nucl.Instr. and Methods. v.165, p.201 (1979).
4) Polarization of the electron beam by hard circular-polarization photons.
Nucl.Instr. and Methods. v.165, p.15 (1979).
5) Laser methods of polarized electrons and positrons obtaining in storage rings.
Proc. of Intern. Symposium on Polarization Phenomena in High Energy Phisics, Dubna,
USSR, p.281 (1982).
6) On the Possibilities of Electron Polarization in Storage Rings by Free Electron Laser.
Nucl.Instr. and Methods. v.193, p.415 (1982).
7) Coherent Electron Cooling Proceedings of 7th Conference on Charged Particle
Accelerators, 1980, Dubna, USSR, p. 269; AIP Conf. Proc. No. 253, p.103 (1992).
8) The electron acceleration by electromagnetic wave in ondulator.
Zh.Tech.Fiz. v.53. p.1317 (1983).
9) The use of the Free Electron Laser for generation of high energy Photon colliding
beams. Dokl.Akadem.Nauk. SSSR v.264, p.849. Zh.Tech Phiz v.53 p.492 (1983).
2
The basic principle of FEL operation
The single-flight regime
At a sufficient length of the undulator entrance radiation is not necessary.
The resonant harmonics of density fluctuations become large and
the bunch can radiate a powerful wave.
The cavity FEL
If the gain per one path through the undulator is small the undulator
is installed in the cavity where the radiation is stored.
3
Particle motion in undulator
Let’s pass electrons through the undulator, whose magnetic field is repeated periodically


in a period 0:
H z   H z   
0
In such fields the induced velocity of electron motion may be written in the from:
 
 
Vs  V E , z ez  V E , z 

Where the velocity components V and transverse components V are the functions of
electron energy E and are periodic with period 0 . To define the parameter of longitudinal
motion mass:
dV
 EV
dE
1
 

The deviation of velocity from induced velocity is V  V I , ,E , z   V I , , E , z 
and to define the important chromatically parameters as
b
E  1, 2 E V
12 

æ 0 E
æ 0 I1, 2
where I and  is the act-phase variables of transverse motion.
If I=0 we have V=0. In helical undulators  and  are follows:
1
2
Q


;


1, 2
2
2
1

V
1

Q
 2
eH
4
Here Q  æ m is undulator parameter.
0
Radiative instabilities of electron beam in undulators
For ultrarelativistic electrons ( >> 1) resonance wavelength of radiation is to follows:
1  Q2
  0
2 2
and is much less then undulator period 0. Radiative increments essentially depend on
the cross size of the beam. There are characteristic quantity
14
   I0 
rtr 


2   02 I 
which distinguishes the narrow and wide beam. Let us write the radiative increment for the
case of a continuous beam (r0  ) . In the case of wide beam (r0 >> rtr ) the increment


 
3  2
2


æ p  0

2 
4 
2
||
1
3
V

Coulomb interaction can be neglected for enough large angle  0 
, when
V
  02   || æ p  . Here is  = 2 c/. In the case of narrow beam radiative increment is
 I  2 02 r02 
  
ln 2 
rtr 
 2 I 
1
2
2 2 2
under condition   0 r0  1 . Coulomb interaction can be neglected.
5
Coherent radiation characteristics
Let's estimate a fraction of the beam energy, converting into radiation for homogeneous
undulator. The particles must shift in longitudinal direction under the influence of
radiation field by a value of the order wavelength:
dV
E
lg ~ 
dE
where lg – is growth length. Thus, the fraction of the beam energy, transformed to
E

radiation is


E
lg
The coherent radiation power for uniform undulator is:

W  E N
lg
Let's notice, that in a non-uniform undultor, the fraction of the energy transformed to
radiation, can be considerably increased using the capture of particles in the wave field
in an autophasing mode.
6
Usage of FEL for fast polarization of electrons in storage rings
Effect is based on the dependence at the Compton scattering cross
section on the initial electron (positron) polarization. In the case of
hard photons the spin dependence is used to knock out mainly
certain helicity from an electron beam in a single scattering. This
method enables one to achieve very short polarization times (of
the order of a few seconds). In the case of fairly soft quanta
alternative method without particle escape from the beam may be
used to polarize the beam. This effect is based on the dependence
of the energy losses in the multiple scattering on the spin direction
together with a spin- orbital coupling in the field of a storage ring.
This coupling is necessary for the beam polarization by soft
quanta.
7
Polarization of electrons in storage rings
by soft circularly polarized photons
e
undulater
accelerator
e
FEL
e
e
Parameters of FEL
E  6 MeV, I  300 A, 0  2 cm, H 0  2,5 kG,   102 cm
1  10 cm, Lundulater  1,5 m, Lbunch  30 cm,   103 rad  cm
Parameters of beam in accelerator
Ebeam  20 GeV ,  polarization  20 min
8
Polarization of electrons in storage rings
by hard circularly polarized photons
e
undulater
accelerator
FEL
e
e
Parameters of FEL
E  0,5 GeV , N e  1012 , 0  2 cm, H 0  5 kG,   2 10 6 cm
1  60 cm, Lundulater  6 m, Lbunch  2 cm,   10 3 rad  cm
Wpeak  1010 W, Wavr  10 kW
Parameters of beam in accelerator
Ebeam  40 GeV ,  polarization  15 sec  P  50%,   20%
9
Method of particle acceleration
by electromagnetic wave in undulator
undulater
This method is based on autophasing well-known
in the theory of accelerators. Effective Hamiltonian
describing autophasing, is similar to Hamiltonian
describing synchrotron oscillation in accelerators:
P2
H
 U s   s cos s  sin  
2
here p = E - Es is energy deviation of equilibrium
particle energy, U s  e s Eˆ is amplitude of
effective potential. This amplitude is proportional to
transverse component of velocity and wave field.
e
Inversed
FEL
e
The effective potential
dependence on the phase.
At linear increase of a field undulator we have
particle acceleration with constant rate:
Es  m Q

2æ0
,
cos s 
m  Q
2e E æ 0
10
Usage of FEL for particle acceleration (transformer of energy )
undulater
undulater
FEL
Accelerator
Electron energy is decrease
Proton energy is increase
e
e
p
p
The numerical example of proton acceleration
(case of cylindrical resonator D=4mm)
Parameters of FEL   103 cm, Wpeak  1012 W
Parameters of proton accelerated beam
Ein  200 MeV, Eout  20 GeV, 0  40 cm, H  0,7  70 kG,
s  30 , Lbunch  3 cm , Laccelerator  400 m .
Acceleration rate
dEproton
dz
MeV
 0,5
cm
11
Usage of the FEL for generation
of high energy photon colliding beams
FELs open practical possibility of obtaining of colliding photon
beams (- quanta) with energy of about 10x10 GeV and luminosity
of about existing colliding electron beams.
Interaction points of - beams
Focusing lens
e
e
undulater
undulater
e
Interaction points of electron
beams and FEL radiations
12
e
Numerical example of - colliding beams (see slide 12)
Parameters of beam in linear accelerator
E
EIP  50 GeV , N e  1012 , Lbunch  1cm,
 10 3 ,
E
Parameters of FEL
E 10 GeV ,
  10 5.
0  20 cm, H 0  20 kG,   4 10 5 cm, f  10 Hz
1  3.4 m, Lundulater  40 m, Lbunch  1cm,   10 7 rad  cm
  WFEL / Wbunch  0,5%.
Spectral luminosity of - beams
 dL 
 0
  1032 cm 2 sec 1
 d0  max
13